Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

We analyze type I vacuum solutions admitting an isometry whose Killing 2--form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group $G_3$ of isometries. We give a classification of this family and we study the Bianchi type for each class. The classes compatible with an aligned Killing 2--form are also determined. The Szekeres-Brans theorem is extended to non vacuum spacetimes with vanishing Cotton tensor.Comment: 19 pages; a reference adde

On the Weyl transverse frames in type I spacetimes

We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.Comment: 12 pages, submitted to Gen. Rel. Grav. (6-3-2004

On the classification of type D spacetimes

We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and non-vacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of spacetimes with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the non-existence of purely magnetic solutions. The usefulness of these results is illustrated in characterizing and classifying a family of Einstein-Maxwell solutions. Our approach permits us to give intrinsic and explicit conditions that label every metric, obtaining in this way an operational algorithm to detect them. In particular a characterization of the Reissner-Nordstr\"{o}m metric is accomplished.Comment: 29 pages, 0 figure

On the separable quotient problem for Banach spaces

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the results presented are consequence of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces c_0 and l_p, for 1 <= p <= \infty. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica

A systematic review and meta-analysis on the effectiveness of exposure and response prevention therapy in the treatment of Obsessive-Compulsive Disorder

Exposure and Response Prevention (ERP) is considered the most effective psychotherapeutic treatment for Obsessive-Compulsive Disorder (OCD). The literature supports its adoption yet results vary and vagueness regarding therapy protocol exists. We present an updated review and meta-analysis to provide clarity in the comparison of strict ERP protocol to control or active therapy groups. Moderator analyses were conducted to investigate treatment effect of cognitive elements, hours of therapy and duration of OCD. A systematic literature search, concluded in January 2021, identified twenty-four studies, published between 1997 and 2018, including a total of 1134 patients. The main analysis assessed the difference between pre-treatment and post-treatment scores compared amongst ERP and the other groups. We found a statistically significant different reduction in pre-treatment to post-treatment Yale-Brown Obsessive Compulsive Scale scores between ERP therapy versus other groups. We also found a statistically significant moderation effect of cognitive elements. The other two moderators, hours of therapy and OCD duration, were non-significant. Our review suggests that ERP was superior to the other groups, including both neutral and active treatments, in reducing OCD symptomatology and should therefore be recommended as an optimal therapy. Future research should focus on tailoring ERP to the individual and investigating further refinements

Failure Handling in BDI Plans via Runtime Enforcement

This project CONVINCE has received funding from the European Union’s Horizon research and innovation programme G.A. n. 101070227. This publication is funded by the European Union. Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or European Commission (the granting authority). Neither the European Union nor the granting authority can be held responsible for themPublisher PD